Cut chicken breasts into small, bite-sized pieces and place into a mixing bowl. Sprinkle the 1 teaspoon cornstarch over the chicken and mix together. Let that sit while you prepare the sauce and cut the bell peppers.
MAKE THE SAUCE: combine all sauce ingredients in a glass measuring cup or a mixing bowl and whisk together to combine.
Heat olive oil in a large skillet pan over medium-high heat. You want the pan hot when you add the chicken. Add the chicken to the hot skillet and cook until chicken is mostly cooked through and white on the outside.
Add the garlic, ginger, and chopped green peppers in with the chicken. You may need to add an additional 1 teaspoon of olive oil to the pan. Stir and cook for about 2 minutes or until the ginger and garlic is fragrant.
Add the sauce into the pan and bring the mixture to a low boil, and then reduce heat to medium-low and let it simmer for about 5-10 minutes.
The sauce will thicken slightly more once it's off the hot stove. Serve over rice.
You can buy fresh ginger in the produce section. Simply take a piece of it and shred it or finely chop it. Or, the easiest thing to do is to buy a tube of the ginger paste which you can find in the refrigerated section of the produce area. If needed, you could also substitute with 1/2 teaspoon ground ginger.
If there is no way you can find Oyster Sauce, you can substitute with thick teriyaki sauce or Hoisin sauce. The flavor will change but it should still be good. But try to find the Oyster sauce cause it adds such a great flavor to the final dish.